Integer Order PI Controller Research Articles

Direct Fractional-Order Adaptive Control Design for Cascaded Doubly-Fed Induction Generator (CDFIG) in a Wind Energy System

This paper is devoted to a fractional-order model reference adaptive control (FO-MRAC) synthesis for the independent control of the active and reactive power flows in the cascaded doubly fed induction generator (CDFIG) in wind energy systems. The proposed adaptive control law combines a second-order-like fractional reference model and a direct MIT adaptation law using a fractional order integrator. This generator configuration can be an interesting alternative to standard double-output wound rotor induction generators. It is made up of two identical wound rotor induction motors such that their rotors are mechanically and electrically coupled. Using two cascaded induction machines permits the elimination of the brushes and copper rings in the traditional doubly-fed induction generator DFIG, which makes the system more resistant and reduces maintenance costs. In the first step, we propose a classical PI controller synthesis to regulate the active and reactive power produced by CDFIG. Then, the FO-MRAC design is realized and a comparative study based on numerical simulations is performed between the classical regulators PI, MRAC, and FO- MRAC, to demonstrate the superiority of the proposed fractional-order adaptive controller relative to conventional integer order PI and MRAC controllers. These results illustrate the reliability and efficiency of the proposed adaptive control scheme.

Application of Quasi-Fractional Order PI Controller to IPDT Plant Control

The paper focuses on the design of a fractional order PI controller (FO-PI) and the verification of the properties of the control loop with an integral plus dead time (IPDT) system. The fractional order integrator in the controller is approximated by the Oustaloup method. The multiple dominant pole method (MDPM) is used to tune the controller parameters. The input parameters for controller tuning are obtained by optimization using the algorithm presented in the paper. The properties of the control loop with the FO-PI controller tuned in this way have been verified by simulation and compared with the properties of the control loop using an integer order PI controller.

Analysis of different control schemes of PMSM motor and also a comparison of FOPI and PI controller for sensorless MSVPWMM scheme

This paper investigated different control Techniques of Permanent magnet synchronous motor (PMSM) drive with open loop, voltage/frequency (V/F) control, closed-loop Space Vector Pulse Width Modulation (SVPWM) control, and sensor-less Modified Space Vector Pulse Width Modulation (MSVPWMM) control with MATLAB/Simulink. The different applications of commercial use require different control schemes due to cost-effectiveness. In a small commercial application where not much precision is required, open-loop or V/F control is used, due to their easy calculation and implementation and becomes a low-cost product outcome. Where their high precision has required closed-loop control is being adopted. In this paper, closed-loop SVPWMM and sensor-less MSVPWM techniques are proposed. The algorithm has a much faster response in the switching of the inverter that is used provides better output has fewer harmonic contents. Fractional order controllers can provide more flexibility in tuning and can better adapt to complex and nonlinear systems. This often leads to improved control performance, especially in systems with unknown or time-varying dynamics. It helps to reduce steady-state error compared to integer order PI controllers. By adjusting the fractional order exponent, the system's characteristics matched better with the controller's response. Also, the FO-PI controllers allow for smoother transitions between different control modes or set points and help to reduce overshoot and rise time in dynamical systems, as they allow for more precise control of the transient response and Constant speed response available at desired load. The control techniques have been modeled and simulated in MATLAB simulation software. The proposed scheme provides efficient performance in steady-state and dynamic load conditions.

Controller Design based on Fractional Calculus for AUV Yaw Control

This research presents a fractional order integral controller strategy, which improves the steering angle for Autonomous Underwater Vehicles (AUVs). The AUV mathematical modeling is presented. A Fractional Order Proportional Integral (FOPI) control scheme is implemented to ensure the yaw angle stability of the AUV steering under system uncertainty. The FOPI controller is validated with MATLAB/Simulink and is compared to the conventional Integer Order PI (IOPI) controller to track the yaw angle of the structure. The simulation results show that the proposed FOPI controller outperforms the IOPI controller and improves the AUV system steering and the overall transient response while ensuring the system's stability with and without external disturbances such as underwater current and different loading conditions.

Dual-Loop Voltage–Current Control of a Fractional-Order Buck-Boost Converter Using a Fractional-Order PIλ Controller

Based on the fact that the inductor and capacitor are of a non-integer order by nature, to provide a more accurate theoretical basis for the optimal control of the converter, the fractional-order model of the Buck-Boost converter in the continuous mode of current is established according to the fractional-order calculus theory. The fractional-order PIλ control system of the fractional-order Buck-Boost converter is designed to compare the performance of the integer-order PI controller with the fractional-order controller. Secondly, the sparrow search algorithm is applied to the optimal design of the fractional-order PIλ control system of the fractional-order Buck-Boost converter to improve the system’s phase margin, stability, and robustness. Finally, the simulation is verified on the Matlab/Simulink simulation platform and compared with the integer-order PI controller.

Combined frequency and voltage regulation in multi-area system using an equilibrium optimiser based non-integer controller with penetration of electric vehicles

The frequency and terminal voltages in power systems are the two critical operating points that balance active and reactive powers, which must be maintained within predefined limits through automatic generation control (AGC) and automatic voltage regulator (AVR) control loops. To address this issue, in this manuscript, the problem of a combined AGC and AVR is solved using a non-integer order PID controller. Its parameters are adjusted using the recently proposed equilibrium optimiser (EO) technique. Along with conventional sources, renewable energy sources such as geothermal power plants and electric vehicles are considered. The EO-tuned non-integer order PID controller outperformed the traditional integer order PI and PID controllers in view of peak overshoots, undershoots and settling times. The performance of EO is evaluated and found superior against widely used particle swarm optimisation and firefly algorithms in the presence of non-integer order PID controller. Different case studies such as random load disturbance, the effect of nonlinearities, the impact of communication time delay and sensitivity analysis have been performed, which also test the heftiness of the non-integer order PID controller. The obtained results are verified using the real-time digital simulator OPAL-RT (OP4510) for nominal conditions.

Conformable Fractional Order Controller Design and Implementation for Per-Phase Voltage Regulation of Three-Phase SEIG Under Unbalanced Load

Self-excited induction generators (SEIGs) usage is an effective way to generate electrical power in off-grid locations. This study aims to performance improvement for voltage regulation of the SEIG in wind turbine systems. To achieve this, a fixed-capacitor with thyristor controlled-reactor based per-phase voltage controller is designed with a conformable fractional order proportional integral (CFOPI) method. The SEIG system is modeled based on small signal analysis by using the input-output data, experimentally. To do this, system identification toolbox of Matlab is used. The proposed controller is established on conformable fractional integral approach proposed by Khalil et al. in 2014. Proposed CFOPI controller parameters Kp , Ki and γ are optimized using particle swarm optimization (PSO) according to minimization of integral time absolute error (ITAE). To validate the success of proposed scheme, CFOPI, traditional fractional order PI (TFOPI) and integer order PI (IOPI) controllers are tested under same experimental setup and results are compared. Three experiments, after voltage build-up process, under balanced and unbalanced load are done for each controller. Experimental results demonstrate that proposed voltage regulator improves the performance of SEIG systems. Moreover, robust voltage regulation is ensured thanks to independent control loops created for each phase.

Design and High-Order Precision Numerical Implementation of Fractional-Order PI Controller for PMSM Speed System Based on FPGA

In this paper, the design of a fractional-order proportional integral (FOPI) controller and integer-order (IOPI) controller are compared for the permanent magnet synchronous motor (PMSM) speed regulation system. A high-precision implementation method of a fractional-order proportional integral (FOPI) controller is proposed in this work. Three commonly used numerical implementation methods of fractional operators are investigated and compared for comprehensively evaluating the numerical implementation performance in this work. Furthermore, for the impulse response invariant implementation method, the effects of different discretization orders on the control performance of the system are compared. The high-order fractional-order controller can be implemented accurately in a control system with the field-programmable gate array (FPGA) with the capability of parallel calculation. The simulation and experimental results show that the high-precision numerical implementation method of the designed high-order FOPI controller has better performance than the ordinary precision fractional operation implementation method and traditional order integer order PI controller.

Identification of gain and phase margins based robust stability regions for atime-delayed micro-grid system including fractional-order controller in presenceof renewable power generation

This study examines the gain and phase margins (GPMs) based robust stability margins in the parameter space of fractional order proportional-integral (FOPI) controller for a micro-grid (MG) system with communication time delays. Fluctuations in renewable energy sources (RESs), uncertainties in parameters of system components and communication delays could adversely affect the dynamical analysis and frequency stability of the MG system. Such a MG system has an interval characteristic due to the parametric variations and the interval transfer functions defined by Kharitonov's theorem, which presents a solution for checking of robust stability. Therefore, this study addresses the robust stability regions containing a set of robust FOPI controller gains for all possible transfer functions of the MG system by a simple graphical method working in controller parameter space. In this way, the impact of fractional order degree of integral controller on the robust stability regions is exhaustively examined by the graphical method. Additionally, robust performance of the interval MG system in terms of design specifications including GPMs is analyzed, and the effect of GPMs on the robust regions is investigated by the graphical method. Results indicate that GPM parameters provide the desirable performances for the MG and fractional order of integral controller considerably increases the robustness of the stability margin of the MG when compared with the integer order PI controller.

Sürekli Mıknatıslı Senkron Motorun Hız Takip Sistemi için Uygun Kesirli PI Kontrolör Tasarımı ve Optimizasyonu

The use of permanent magnet synchronous motor (PMSM) is increasing rapidly to meet the need to increase efficiency in variable speed drive systems used in the industry, in recent years. This paper aims to improve the speed control performance of the PMSM based systems. To achieve this, a PMSM speed controller is designed based on the conformable fractional order proportional integral (CFOPI) method. CFOPI controller coefficients kp, ki and γ are optimized using response surface method (RSM). To validate the success of the proposed scheme, the CFOPI controller and the integer order PI (IOPI) controller are tested under the same simulation model and the results are compared. The proposed method grants robust performance with less computational load then the classical fractional order controllers for variable referenced PMSM speed tracking systems. The CFOPI controller can be applied easily for industrial variable speed drive systems which is using PMSM to improve the performance and stability of the systems.

Enhanced equilibrium optimization method with fractional order chaotic and application engineering

In this study, enhanced equilibrium optimization (E2O) algorithm was proposed by developing stochastic processes in equilibrium optimization (EO) method with fractional order chaotic (FOC) system models. FOC model was firstly used in an optimization algorithm in this study. System responses of the fractional order chaotic models were used instead of random coefficients in the basic EO method. The performance of many fractional order chaotic system models was tested on benchmark functions. It was experimentally determined fractional order chaotic models of Genesio Tesi, Chua Memristor and cellular neural network which were convenient for the EO method. Model coefficients and initial conditions of corresponding fractional order chaotic models were obtained for benchmark functions to find suitable models for E2O algorithm. In order to present engineering application performance of the proposed E2O method, controller parameters were optimized for liquid level control that was decoupled two-input and two-output (TITO) tank system. Fractional and integer order PI and PID controllers’ parameters were tuned according to the reference input signals for TITO tank system. Multi-objective function was defined with mean square error (MSE) definition as system’s overall objective function. Proposed multi-objective function was minimized during to optimization process. E2O algorithm results were compared with each other and existing literature studies results. In this way, it was shown comparatively that usage of fractional order chaotic models in the proposed E2O algorithm affected optimization algorithm performance and produced better results.

Design and Control of Grid-Connected PWM Rectifiers by Optimizing Fractional Order PI Controller Using Water Cycle Algorithm

In this paper water cycle algorithm-based fractional order PI controller (FOPI) is proposed for virtual flux-oriented control of a three-phase grid-connected PWM rectifier. FOPI controller makes the PWM rectifier control more robust due to the fractional behavior. Fractional-order controllers have an additional degree of freedom, so a wider range of parameters is available to provide better control and robustness in the plant. The optimization and design of the FOPI controller are done using the water cycle algorithm (WCA). WCA is an optimization method inspired by monitoring the water cycle operation and flow of water bodies like streams and rivers toward the sea. The performance of the FOPI controller is compared with the classical integer order PI controller. The parameters of PI and FOPI controllers are optimized and designed using the WCA technique, leading to WCA-PI and WCA-FOPI controllers. The system is tested using MATLAB/Simulink. The simulation results verify the better performance of WCA-FOPI in terms of settling time, rise time, peak overshoot, and Total Harmonic Distortion (THD) of grid current. A robustness measurement with line filter parametric variations and non-ideal supply voltage (unbalance and distorted supply voltage) is carried out. The WCA-FOPI demonstrates more robustness as compared to WCA-PI. Simulation findings validate the WCA-FOPI controller outcomes as compared to WCA-PI in terms of control effect and robustness.

Fractional Order Model-Based Design of Controllers for Improved Operation of Wastewater Treatment Plants

A non-integer order model is developed for a biological wastewater treatment plant (WWTP) represented in benchmark simulation model (BSM1) scenario. In BSM1 framework, sufficient nitrification is maintained by providing a constant aeration flow rate, by controlling the dissolved oxygen (DO) in the fifth reactor at pre-selected set-point. The nitrates in the anoxic reactor-2 are controlled by manipulating internal recirculation flow. Initially, a state-space model for both the loops is developed by varying both the manipulated variables by ± 10% around the nominal operating point. Then, fractional order models are developed for both the loops around the operating point. After obtaining the fractional order model, fractional IMC-PID-based controllers are designed for controlling the WWTPs. The designed fractional order simple PI controllers provided improved plant as well as controller performance when compared to the traditional integer order PI controllers.

Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes

Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

Fractional-Order PI Control of DFIG-Based Tidal Stream Turbine

This study mainly investigates the current and speed control strategies of a doubly-fed induction generator (DFIG), which is applied to a tidal stream turbine (TST). Indeed, DFIG using integer-order PI (IOPI) controller has been widely proposed in the applications with a similar system, especially in wind energy conversion system (WECS). However, these conventional controllers cannot deal with the problems caused by the parameter variations satisfactorily under complex and harsh operation conditions, and may even deteriorate the performance. As a result, a fractional-order PI (FOPI) controller is considered to improve the efficiency and performance of DFIG-based TST in this paper. The FOPI controller, developed from the traditional IOPI controller and the fractional calculus theory, has a lot of prominent merits in many aspects, such as robustness, stability, and dynamic performance. In this paper, the proposed control strategies are embedded into the whole TST model which contains the tidal stream turbine, and the generator. The obtained simulation results demonstrate the prominent effectiveness and advantages of the proposed strategies compared with the conventional IOPI controller in terms of overshoot, static error, adjustment time, and robustness. It implies that FOPI controller could be a good candidate in TST applications.

A Study of the Influence of Stochastic Fractional-Order Delay Dynamics in a Networked Control System

Stochastic communication delays are present in networked control systems and have a significant influence over its closed-loop performance and stability. These delays are time-variant and have infinite variance, indicating fractional-order behavior that can be modeled using α-stable distribution. This paper presents a quantitative analysis of the effects of fractional-order α-stable distribution random communication delays in a networked control system for a temperature control application. The networked closed-loop system assessment is performed using four different controllers. Two integer order PI controllers tuned using classic tuning methods, and two fractional-order PI controllers tuned using standard tuning rules for fractional-order system. One hundred numerical simulation experiments are performed, modeling the random communication delays between the plant and controller using an α-Stable distribution with different α values. Obtained results show that fractional-order controllers can deal better with time-variant fractional-order random communication delays that follows an α-Stable distribution compared with the integer-order controllers.

Design of fractional order proportional integral controller for load frequency control of multi area power system under deregulated environment

The main objective of presented article is here to focus how efficiently minimise the deviations in frequency and area control error caused by load fluctuations and uncertainties in load under the deregulated power system. This work is carried out to eliminate the frequency errors by using fractional order proportional integral (FOPI) controller under deregulated environment by considering the effect of one possible bilateral contract scenario. Because of system nonlinearities, uncertainties and continuously fluctuant load demand the design of these controllers is quite complicated in deregulated environment. The proposed work is to enhance the system parameters like transmitted line power, frequency deviation error, and area control error (ACE) using fractional order PI controller for hydro-thermal system and thermal-thermal system under deregulated environment. The results have been analysed with classical integer order PI controller and FOPI controller. It is observed that the efficacy of the results is satisfied and improved when compared with previous work.

Design of fractional order proportional integral controller for load frequency control of multi area power system under deregulated environment

The main objective of presented article is here to focus how efficiently minimise the deviations in frequency and area control error caused by load fluctuations and uncertainties in load under the deregulated power system. This work is carried out to eliminate the frequency errors by using fractional order proportional integral (FOPI) controller under deregulated environment by considering the effect of one possible bilateral contract scenario. Because of system nonlinearities, uncertainties and continuously fluctuant load demand the design of these controllers is quite complicated in deregulated environment. The proposed work is to enhance the system parameters like transmitted line power, frequency deviation error, and area control error (ACE) using fractional order PI controller for hydro-thermal system and thermal-thermal system under deregulated environment. The results have been analysed with classical integer order PI controller and FOPI controller. It is observed that the efficacy of the results is satisfied and improved when compared with previous work.

Robust fractional-order auto-tuning for highly-coupled MIMO systems

Many processes in industry are highly-coupled Multiple-Input Multiple-Output (MIMO) systems. In this paper, a methodology, based on the Kissing Circle (KC) tuning method, is proposed to tune a fractional-order PI controller for these types of systems. The KC method relies on frequency domain specifications and emphasizes improving robustness. The method does not require a model, a single sine test suffices to obtain the controller parameters. Hence, the method can be categorized as an auto-tuner. For comparison, an integer-order PI is tuned with the same requirements. To evaluate and analyze the performance of both controllers an experimental test bench is used, i.e. a landscape office lighting system. A direct low-order discretization method is used to implement the controller in a real process. Both controllers are subjected to simulation experiments to test the performance in time and frequency domain and they are subjected to process variations to evaluate their robustness. The fractional controller manages to control a process that is susceptible to 85% variation in time constant mismatch as opposed to 79% for the integer-order controller. An Integer Absolute Error evaluation of experimental results show that the fractional-order PI controller and integer-order PI controller have similar control performance, as expected from the frequency domain analysis. As model uncertainty can add up in MIMO systems, improved robustness is crucial and with this methodology the control performance does not deteriorate. Moreover, a decrease in power consumption of 6% is observed.

Enhancement of Power System Transient Stability By Fractional Order Controlled STATCOM Tuned By PSO

This paper discusses the application of Fractional order PI controlled Static synchronous compensator for improvement rotor angle stability of inter connected power system. FACTS Controllers plays important role in enhancing the power system stability.Besides improving the stability margin of the power system it also aids the damping of inter area power oscillations. In the present work STATCOM is connected in multimachine power system .The dynamic response of the STATCOM is controlled by using fractional order controllers.The controller gains of the fractional controller are tuned by using PSO algorithm.It gives acceptable solutions to continuous non-linear systems with less computational effort. The performance of the proposed controller has been compared with integer order PI controllers at different locations of fault. In this paper a 3 machine 9 bus WSSC test power system is considered and simulated in MATLAB/SIMULINK.